AP Kayle offers two major utilities that greatly increase the options for a Kayle player because of these, I have never been out CS'd while playing AP Kayle with this build in the past year. Her lane dominance stems from her AOE damage on her E and her heal for lane sustain. These all scale with AP, and allow the player to make money, shut down their lane opponant, and get items quicker than the other players.

AD Kayle has become the common build used by most Kayle players. AD Kayle was mathematically shown to do more damage in the end game to a single opponent. Believe it or not, the strength of a build does not only lie in the amount of damage you can deal to a single enemy champion. Who knew!?

(E) Righteous Fury AOE: Kayle's E does AOE damage based on Ability Power + direct single target damage based on Attack Damage. The AOE gives AP Kayle Players well above 150 minion farm in average-length games, and allows the Kayle to instantly push a lane and create passive-offensive pressure.

(W) Divine Blessing: Kayle's W is not just a speed boost, but is also a very strong heal that should have been calculated in the damage output difference between AP and AD Kayle, but wasn't. As an added Utility, the heal is not just a self heal, but can save the lives of others.

AP Kayle has negligible/no mana problems, unlike AD Kayle. Along with the improved Divine Blessing, AP Kayle does not need potions to regenerate health, and can stay in lane longer.
AP Kayle includes more Cooldown Reduction in her build, so Righteous Fury, Divine Blessing, and even Reckoning can be used more often, for more damage output.

AP Kayle caps her damage output at a lower single target value, so in the case of a drawn out and stalemated game, AD Kayle offers a greater damage output.
-This happens rarely, but must be accounted for. I do not remember the last time I triple potted.

I recommend binding your Ability Keys to smartcast so you may cast them quickly, and binding each Shift+Ability Key to selfcast. AP Kayle is a champion which does massive dps, while healing/saving herself and others. This abilities must be used very quickly.

Doran's Ring: This beginning item allows Kayle to not run low on mana, and to spam her W after poking with her E. This makes AP Kayle one of the strongest laners in the game. She can 1-on-1 most champions at level 1, AD or AP, just to replenish health at level 2.

Berserker's Greaves: Give you the movement speed and attack speed which allows you to get many hits on a fleeing opponent, after hitting W, as they turn their back. <- Do this. A lot.

Malady: Gives attack speed and damage output which allow you to farm extraordinarily well, and obtain your items faster than other champions.

Nashor's Tooth: 65 AP!, more AS, more CDR, and money efficient too.

Runaan's Hurricane: Gives insane AS, near instantly maxing Malady and Passive MR shred. Missiles apply on-hit effects DOUBLING single target DPS from them.

Rabadon's Deathcap: More AP for more AOE damage, more heals, more Malady damage, and even more Q nuke power.

From here on you can buy any item in place of your Doran's Ring. I recommend Zhonya's Hourglass, Abyssal Scepter, Frozen Mallet, or Banshee's Veil because they all aid your damage output, while giving you that bit of toughness needed in the end-game. This item should counter your strongest damaging opponents, in order to win the fight for the final push.

Flat AS Marks: Give you massive bonus attack speed from level 1 and on. This is incredible for level 1-on-1s or team fights, and makes a difference late in the game as well.

Flat Mana-Regen Seals: Give mana regen with provides Kayle with (W) spam early on, and a very strong sustain.

Flat AP Glyphs: Gives 10.8 AP at level 1 and on. Destroys in level 1 fights mixed with AS Marks.

Flat HP Quints: Gives extra health in the early levels. Is a very common quint, so it is likely you have them. Any of the above runes would be good quints as well.

The end-game is all about the early-game.